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M. Lázaro¹, C.F. Casanova², P. Fajardo³ and P. Martín¹

¹Department of Continuum Mechanics and Theory of Structures, Polytechnic University of Valencia, Spain
²Department of Applied Physics, University of Granada, Spain
³Department of Bioengineering and Aerospace Engineering, University of Carlos III, Madrid, Spai

Keywords: viscoelastic damping, complex eigenfrequencies, recursive method, proportional damping.

Summary

Materials of viscoelastic nature are widely used for engineering applications such as vibration isolation or as devices to mitigate earthquake effects in buildings. In order to predict the behavior of such structures, the models must reproduce the response as accurately as possible. In the most general case, the structures that include viscoelastic materials are characterized by hereditary energy dissipation mechanisms: the damping forces depend on the history of the velocity response. Mathematically, this fact is represented by convolution integrals that involve the velocities of the degrees of freedom over certain kernel functions. Many real structures modeled by these motion equations present a proportional (or lightly nonproportional) damping matrix, that is, the damping matrix becomes diagonal (or diagonally-dominant) in the modal space of the undamped problem. This paper describes the development a new numerical method to compute the eigenvalues of linear viscoelastic structures with proportional (or lightly nonproportional damping). The key idea is to build two complexvalued functions of a complex variable, whose fixed points are the eigenvalues. Theoretical results are illustrated with a numerical example where the described properties of convergence are shown.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 105 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: Paper 35 Recursive Computation of Complex Frequencies of Vibrating Non-Viscous Damped Systems M. Lázaro¹, C.F. Casanova², P. Fajardo³ and P. Martín¹ ¹Department of Continuum Mechanics and Theory of Structures, Polytechnic University of Valencia, Spain ²Department of Applied Physics, University of Granada, Spain ³Department of Bioengineering and Aerospace Engineering, University of Carlos III, Madrid, Spai doi:10.4203/ccp.105.35 purchase the full-text of this paper Full Bibliographic Reference for this paper , "Recursive Computation of Complex Frequencies of Vibrating Non-Viscous Damped Systems", in , (Editors), "Proceedings of the Ninth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 35, 2014. doi:10.4203/ccp.105.35 Keywords: viscoelastic damping, complex eigenfrequencies, recursive method, proportional damping. Summary Materials of viscoelastic nature are widely used for engineering applications such as vibration isolation or as devices to mitigate earthquake effects in buildings. In order to predict the behavior of such structures, the models must reproduce the response as accurately as possible. In the most general case, the structures that include viscoelastic materials are characterized by hereditary energy dissipation mechanisms: the damping forces depend on the history of the velocity response. Mathematically, this fact is represented by convolution integrals that involve the velocities of the degrees of freedom over certain kernel functions. Many real structures modeled by these motion equations present a proportional (or lightly nonproportional) damping matrix, that is, the damping matrix becomes diagonal (or diagonally-dominant) in the modal space of the undamped problem. This paper describes the development a new numerical method to compute the eigenvalues of linear viscoelastic structures with proportional (or lightly nonproportional damping). The key idea is to build two complexvalued functions of a complex variable, whose fixed points are the eigenvalues. Theoretical results are illustrated with a numerical example where the described properties of convergence are shown. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £45 +P&P)
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